Algebra Examples

$x - 3 y = 0$ $y = \frac{1}{3} x + 2$

Step 1

Add $3 y$ to both sides of the equation.

$x = 3 y$

$y = \frac{1}{3} x + 2$

Step 2

Replace all occurrences of $x$ with $3 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $y = \frac{1}{3} x + 2$ with $3 y$ .

$y = \frac{1}{3} \cdot (3 y) + 2$

$x = 3 y$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Factor $3$ out of $3 y$ .

$y = \frac{1}{3} \cdot (3 (y)) + 2$

$x = 3 y$

Step 2.2.1.2

Cancel the common factor.

$y = \frac{1}{3} \cdot (3 y) + 2$

$x = 3 y$

Step 2.2.1.3

Rewrite the expression.

$y = y + 2$

$x = 3 y$

$y = y + 2$

$x = 3 y$

$y = y + 2$

$x = 3 y$

$y = y + 2$

$x = 3 y$

Step 3

Solve for $y$ in $y = y + 2$ .

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Step 3.1

Move all terms containing $y$ to the left side of the equation.

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Step 3.1.1

Subtract $y$ from both sides of the equation.

$y - y = 2$

$x = 3 y$

Step 3.1.2

Subtract $y$ from $y$ .

$0 = 2$

$x = 3 y$

$0 = 2$

$x = 3 y$

Step 3.2

Since $0 \neq 2$ , there are no solutions.

No solution

$x = 3 y$

No solution

Step 4